I am given a curve/path $\mathcal C$:
$ x=2\cos u$ and $ z=2\cosh u$ where $ 0\le u \le \frac{\pi}{2} $
The surface of rotation $\mathcal A$ is given by rotating $\mathcal C$ around the Z-axis.
Now what I'm having troubles understanding is for the curve $\mathcal C$, is y=0? or is it equivalent to some constant?
Now, for finding an equation for $\mathcal A$, do I need to transfer $\mathcal C$ to Cartesian/non parameter form first?
Implicitly the curve $\mathcal C$ lies in the plane $y=0$ and the surface $\mathcal A$ has for parametric equations
$$A(u,\theta) \equiv \begin{cases} x &= 2 \cos u \cos \theta\\ y &= 2 \cos u \sin \theta\\ z &= 2 \cosh u \end {cases}$$